Dynamics (3.2.1)

The net force acting on an object is a single force that acts as the sum of all forces acting on an object. In this way, it describes the net effect of all the forces acting on an object. As each force acting on an object has a magnitude and direction, the net force is the vector addition of all of the forces present.

The direction and magnitude of the net force determine whether the object will accelerate:

• If the forces on an object are balanced (net force is zero), the object will not accelerate – it will either remain stationary or move at a constant velocity.

• If the forces are unbalanced (there is a nonzero net force), the object will accelerate in the direction of the net force.

An object in free fall is one that is falling solely under the influence of gravity. In the absence of air resistance, all objects experience the same acceleration due to gravity regardless of their mass.

David Scott famously proved this during the Apollo 15 mission to the moon, where a dropped hammer and feather reached the ground at the same time.

Mass vs. weight. In everyday language, someone might say, “I weigh ." However, this is technically incorrect:

• Mass is a scalar quantity measured in kilograms. It represents the quantity of matter that an object is made up of.
• Weight is a vector quantity. It is a force, measured in newtons, that an object experiences due to its location in a gravitational field.

An object’s mass is constant, but its weight varies depending on the strength of the gravitational field in which it is. For instance, the gravitational field strength on the Moon’s surface is , which means an object’s weight is approximately one-sixth what it would be on Earth.

Tension is the force exerted along a stretched object, such as a string, rope, or cable, when it is pulled tight by forces acting from opposite ends. It is uniform throughout an ideal massless, inextensible string. If the string has mass, the tension varies along its length.

Tension requires two forces acting in opposing directions on an object; this is what causes it to stretch and become taut.

An example of this is in a pulley system, where the tension in the rope transmits force between different objects, such as lifting a mass.

The normal contact force is the force exerted by a surface perpendicular to an object in contact with it. It arises from the contact between two solid surfaces and prevents objects from passing through each other. It is always directed perpendicular to the surface and acts away from it.

For example, a book resting on a table experiences a normal contact force equal to its weight. The table pushes up against the book, balancing the force of gravity.

The normal force is not always equal in magnitude to the weight of the object. It equals the weight only when the object is resting on a horizontal surface and no other vertical forces act on it. On an inclined plane, the normal force is less than the object’s weight.

Similarly, the normal force does not always act in the opposite direction to the weight. The normal force is always perpendicular to the surface.

Upthrust, or buoyant force, is the upward force exerted by a fluid (liquid or gas) that opposes the weight of an object submerged in it. It acts vertically upwards, opposing the force of gravity.

An example of this is a boat floating on water experiences upthrust, which keeps it afloat. If the upthrust is equal to the boat’s weight, it remains at rest.

If the upthrust is greater than the object’s weight, the object rises; if less, the object sinks.

Upthrust is determined by the volume of fluid displaced, not the object’s weight. According to Archimedes’ principle, upthrust equals the weight of the displaced fluid, which depends on the fluid’s density and the volume displaced.

For an object fully submerged in a fluid, upthrust, is given by:

Where:

• is the density of the fluid measured in ,
• is the volume of the object displaced measured in , and
• is the gravitational acceleration.

Note that the upthrust force depends on the volume of the object and the density of the fluid, not directly on the mass of the object. A large but light object may experience more upthrust than a small, heavy one.

Friction is the force that opposes the relative motion or the tendency for motion between two surfaces in contact.

Friction acts parallel to the surface and opposite to the direction of motion or attempted motion. It causes energy dissipation in the form of heat and wears down surfaces over time.

An example of this is when pushing a box across a floor, friction between the box and the floor resists its movement.

A free-body diagram is a simplified representation of an object and the forces acting on it. It helps analyse the object’s dynamics by clearly showing all external forces acting on it, their directions and magnitudes.

Free-body diagrams are very useful for solving problems and understanding how different forces interact. Only the forces acting on the object are shown, not the forces the object exerts on other objects.

Forces are represented as arrows originating from the object, with:

• length indicating the relative magnitude of the force (longer arrow = greater force)
• direction indicating the direction in which the force acts.

Each force is labeled with its type and its magnitude if known.

Free body diagrams help in setting up equations using Newton’s laws of motion to solve for unknown forces or accelerations. They are crucial in problems involving objects on inclined planes, where forces must be resolved into components parallel and perpendicular to the incline.

When adding forces at an angle, always remember to label both the angle of application and the direction of the force with an arrow.

In the example above, the weight of a block on an inclined plane has been resolved into the weight force parallel to the slope, , and the weight perpendicular to the slope, .

If a constant force is applied to an object, the object will undergo a resulting acceleration, which will induce it to move. This motion can be studied in either one or two dimensions, such as along a flat surface or on an inclined plane.

• In one-dimensional motion, movement occurs either vertically (up and down) or horizontally (left and right).

• In two-dimensional motion, such as on a slope, both vertical and horizontal directions are involved. When dealing with slopes, it is often easier to resolve forces into parallel and perpendicular components rather than horizontal and vertical components.

A force acting at an angle to a surface can be split into two components.

Parallel component :

This is the component of the force acting along the surface (in the direction of motion on an incline).

Perpendicular component :

This is the component of the force acting perpendicular to the surface (typically balanced by the normal force in an inclined plane problem).

In the diagram above, the weight of a block on an inclined slope may be resolved into parallel and perpendicular components to the slope.

The normal force and act perpendicular to the slope, while acts parallel to the slope.